Raoult's Law Calculator

Raoult's Law Calculator – Vapor Pressure & Composition for Ideal Mixtures

Raoult's Law describes how individual components in an ideal liquid mixture contribute to the total vapor pressure above the solution. This free online Raoult's Law calculator instantly computes partial pressures, total pressure, and vapor-phase compositions for systems with 2 to 5 components. Use it for thermodynamics coursework, distillation design, or vapor-liquid equilibrium (VLE) analysis.

The calculator supports direct vapor pressure input, the Antoine equation for temperature-dependent calculations, and an optional non-ideal mode with activity coefficients — covering everything from textbook ideal mixtures to more realistic systems.

What is Raoult's Law?

Published by French chemist François-Marie Raoult in 1887, Raoult's Law states that the partial vapor pressure of a component above an ideal solution is proportional to its mole fraction in the liquid phase:

P_i = X_i × P°_i

where X_i is the liquid-phase mole fraction of component i, P°_i is the pure-component vapor pressure at that temperature, and P_i is the resulting partial pressure. Summing across all components gives the total pressure:

P_total = Σ P_i = Σ (X_i × P°_i)

The vapor-phase mole fraction of each component (Dalton's Law) is then:

y_i = P_i / P_total

Raoult's Law holds for ideal solutions — typically mixtures of structurally similar compounds such as benzene–toluene or hexane–heptane.

How to Use This Calculator

Set the number of components (2–5) and choose your preferred pressure unit (atm, bar, torr/mmHg, kPa, or Pa). For each component:

1. Enter a component name (optional but helpful for labeling results).
2. Enter the mole fraction X_i. Values are auto-normalized if they do not sum to exactly 1.
3. Enter the pure-component vapor pressure P°_i in the chosen unit, or switch to Antoine mode and provide temperature plus Antoine constants A, B, C. Built-in presets are available for water, ethanol, benzene, toluene, acetone, methanol, hexane, and more.
4. Optionally enable non-ideal mode to enter activity coefficients γ_i (default = 1 for ideal behavior).

Click Calculate to see partial pressures, total vapor pressure, vapor compositions, and for binary systems, a full P–x–y diagram and VLE curve.

Worked Example: Benzene–Toluene Mixture

Consider a binary mixture at a temperature where benzene has a vapor pressure of 100 torr and toluene has 40 torr:

Component   X_i   P°_i      P_i         y_i
Benzene     0.4   100 torr  40.0 torr   0.667
Toluene     0.6    40 torr  24.0 torr   0.333
─────────────────────────────────────────────
Total       1.0    —        64.0 torr   1.000

The vapor is enriched in the more volatile component (benzene, y₁ = 0.667) compared to its liquid composition (X₁ = 0.4). This is the principle exploited in fractional distillation.

Antoine Equation for Temperature-Dependent Calculations

When temperature is known, the pure-component vapor pressures can be calculated automatically using the Antoine equation:

log₁₀(P°) = A − B / (T + C)

where T is in Celsius and P° is in mmHg. Enable Antoine mode, select a preset substance or enter custom A, B, C constants, and provide the system temperature. The calculator converts the resulting mmHg vapor pressure to your chosen output unit.

Non-Ideal Solutions and Activity Coefficients

Real liquid mixtures deviate from ideal behavior due to differences in molecular interactions. The modified Raoult's Law introduces an activity coefficient γ_i:

P_i = X_i × γ_i × P°_i

• γ_i = 1: Ideal behavior (classic Raoult's Law).
• γ_i > 1: Positive deviation — mixture less stable than ideal (e.g., ethanol–water).
• γ_i < 1: Negative deviation — mixture more stable than ideal (e.g., acetone–chloroform).

Positive deviations can lead to minimum-boiling azeotropes (constant-boiling mixtures), which are a key challenge in distillation design.

Binary P–x–y Diagram and VLE Curves

For two-component systems, this calculator generates a pressure-composition (P–x–y) diagram that plots total pressure and each component's partial pressure against liquid mole fraction X₁. A second chart shows the vapor-liquid equilibrium (VLE) y₁ vs X₁ curve. A 45° diagonal represents a non-separating azeotrope baseline — points above it mean the vapor is richer in component 1 than the liquid.

Pressure Unit Conversions

All calculations are performed internally in mmHg and converted to your chosen display unit. Common conversion factors:

1 atm = 760 mmHg = 101.325 kPa = 1.01325 bar = 760 torr

Applications of Raoult's Law

• Distillation design — determining relative volatility and theoretical stages
• Bubble point and dew point calculations for process engineering
• Colligative properties — vapor pressure lowering by a non-volatile solute
• Environmental chemistry — predicting evaporation rates of multicomponent solvents
• Pharmaceutical formulation — solvent selection and drying calculations